Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R. Assertion A: If the A.M. and G.M. between two numbers are in the ratio m : n, then the numbers are in the ratio m + : m - Reason R: If each term of a G.P. is raised to the same power, the resulting sequence also forms a G.P. In the light of the above statements, choose the correct answer from the options given below:

Both A and R are true but R is not the correct explanation of A Explanation: 1. Analysis of Assertion A Let the two numbers be and . The Arithmetic Mean (A.M.) is and the Geometric Mean (G.M.) is . Given the ratio: Using Componendo and Dividendo : Taking the square root on both sides: Applying Componendo and Dividendo again: Squaring both sides: Assertion A is True. 2. Analysis of Reason R Let a G.P. be . If each term is raised to the power , the sequence becomes: This is a new G.P. with first term and common ratio . Reason R is True. 3. Conclusion Both statements are mathematically correct. However, Reason R discusses the properties of a G.P. sequence under exponentiation, while Assertion A is a specific result regarding the ratio of two numbers based on their A.M. and G.M. Reason R does not explain why the ratio in Assertion A is derived. Correct Answer: Both A a

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CUET PG 2023 — Mathematics PYQ

CUET PG | Mathematics | 2023

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: If the A.M. and G.M. between two numbers are in the ratio m : n, then the numbers are in the ratio m + $m^{2} - n^{2}$ : m - $m^{2} - n^{2}$

Reason R: If each term of a G.P. is raised to the same power, the resulting sequence also forms a G.P.

In the light of the above statements, choose the correct answer from the options given below:

Choose the correct answer: